I write today to commemorate the man who inspired the Pennsylvania Mathematics Initiative: Kenneth I. Gross. Ken passed away in September, after a long life of mathematical and education contributions. Chief among the education is his founding of the Vermont Mathematics Initiative, which served as a model for PMI. When George Andrews was looking for a program that could make a difference in the quality of elementary math education, it was VMI’s content-focused approach that he found most promising.

I first visited Ken’s program in the summer of 2012 when the idea of starting a similar program at Penn State was proposed to me. He and the rest of the facilitators welcomed me with open arms, and within an hour or two I had me helping with the workshop. It was inspiring to see the excitement and enthusiasm that everyone shared, and I am happy that I have been able to capture that to bring to Pennsylvania. Ken generously offered me a chance to “run with the big kids,” so to speak, when he invited me to co-teach a week-long workshop with him and Cyndi Garvan in Levy County, Florida in 2013. This was my trial by fire, as I was to run our first PMI workshop a month later with the same materials. I remember the experience and car-trips with Ken fondly.

Ken shared his materials freely with me, for the sake the teachers of Pennsylvania, and was willing to gamble on a young buck like me to modify and rewrite large parts of them. He asked me to act as co-author for the textbook he was writing for VMI, but I regrettably could not devote the time it needed. I wish now that I could have spent more time working on it with him, even if we hadn’t finished it in time, just to have had more time to talk with him and learn from his experiences.

While I only knew Ken for five years, he has been a tremendous influence on my life and PMI in general. He always had time to talk, and took an interest in my life outside my career. He sent me congratulation cards when my daughters were born, and always spoke fondly of his own two daughters. He was a wonderful mentor, a terrific advisor, and a good friend. He absence will be felt as PMI continues in his memory.

PMI’s growth since its first workshop in 2013. Totals account for that summer’s workshops, accrued over all sites. 2016 involved 3 sites, 2017 involved 4.

Summer 2017 at a glance:

Workshops at 4 different Penn State campuses, facilitated by 10 Penn State faculty members

245 hours of instruction

95 participants from 37 school districts across Pennsylvania

We offer a hearty “Thank you” to all of our supporters. We could have never done all of this without the contributions from Earth and Space Science Partnership and NSF award DUE-0962792, the PSU Math Department (University Park), the Eberly College of Science, the College of Education, the office of the Vice Chancellor of Commonwealth Campuses, and the Penn State Provost’s office.

We started the morning with the post-assessment and beliefs survey. The analysis of that data will be shared later this summer.

We then spent some time refreshing the addition and subtraction of signed numbers, and representing that with joining and taking away piles of color-coded counters. That discussion progressed into exploring the multiplication of signed numbers. We found that when one or two of the factors are positive whole numbers, then we can rely on the “__ groups of size ___” model. However, when both factors are negative we need to rely on logic and the distributive property in particular. We ultimately had three explanations: one based on patterns, one based on the notion of the opposite, and one based on comparing the products 4×4 and the expanded form of (5+(-1))x(5+(-1)).

We then split into teams of 3 to do “Bungee Barbie” and started analyzing the data over lunch. Here is the winning drop: https://photos.app.goo.gl/TJO0BwptyT0slWrm2 . After the drops, we debriefed on the mathematical thinking and topics that occurred within that task.

We then got into our “Kumbaya” circle and reflected on what we learned about mathematics, what we learned about teaching, and our commitments to how we can improve our own classrooms. We then read “Hooray for Diffendoofer Day.” The key take-away message: Teach your students to think and the tests will take care of themselves.

Homework

Continue to give your students the best educational experiences possible. Continue to learn how to make those experiences richer, and continue to seek out why of mathematics.

Worked in grade level groups to made a big iceberg poster about linear relationships. How do the concepts we teach at each grade level build floating capacity for engaging with the candle burning problem?

Discussed parents and families, using the message from Cathy Seeley’s book.

We started the day with meeting the returning participants. We then moved to reviewing the homework at our tables. We proceeded to discuss some student work on the Hourglass Problem, and then the Punch Problem and attending to precision.

In the afternoon we discussed the importance of using rich problems (and keeping them rich when they meet the classroom). We then joined up with the returning participants and found out how they implemented what they’ve learned at PMI.

Homework

Make an attempt at the “Two Routes” problem, including the Going Further section.

In questioning small groups of students working on a problem, a teacher noticed that when she asked a “focusing” question, the students continued to look at their work and continued to engage in their own dialogue. When she asked a “funneling” question, the students looked up at the teacher. Comment on these observations.

Listen to your audiorecording from today. Use fig. 14 on p. 36 and fig. 16 on p. 39 to write a description of your question patterns.

How might you change your questioning to elicit and then use evidence of your students’ thinking to move the student forward to the mathematical goal of the problem?

Try the Maze Playing Board. Let’s see who has the largest value tomorrow. There MAY be a prize involved.

Build stamina; start where they are; “Think” stage – start with a few seconds and then build up.

Ask students to make a plan before starting “solving”

Decorate your room with people who succeeded after “failing” several times.

Have “hip pocket” responses “what are you thinking?”

Figure out where kids might have struggles with the task.

Stop talking so much.

Make sure you have manipulatives available

Have anchor charts

Broke up into grade-level groups and began planning a “first-day lesson” by anticipating student responses

For tomorrow:

Read the Message called “Upside-down teaching”

In your notebook, complete respond to the discussion prompts for teachers at the end of the message (on p. 94). Try to make connections about what we’ve read about and discussed so far in PMI.

Many thanks to Kimberly for baking some delicious chocolate zucchini bread. Her recipe is below. (Bonus question: If you only want to make a half a loaf, how much shredded zucchini do you need? Write the number sentence to describe that scenario.)

Review the “Beliefs about teaching and learning mathematics” chart (p. 11, Obstacles). What beliefs are evident in Ms. Flahive’s and Ms. Ramirez’s classrooms (see fig. 21 on page 51)? What impact do those beliefs have on students’ opportunities to grapple with the mathematical ideas and relationships in the problem?